Use

When the Tonsil Stone is in the Hunter's inventory, a Lesser Amygdala, in the Cathedral Ward, will teleport the Hunter to the Lecture Building on the 1st floor. To reach the room with the Lesser Amygdala, take a left at the bottom of the first set of stairs after exiting the Grand Cathedral, in the Cathedral Ward. Continue past the area with the well and down a few ramps passing two Executioners. The second Executioner stands near the entrance to the room with the Lesser Amygdala.

Walking up to the door in the room will trigger a vortex animation and the Lesser Amygdala will grab the Hunter, followed by a cut scene. Note that no Blood Echoes will be lost and +2 Insight will be gained. This can be used to reach the Nightmare Frontier faster for a player that wishes to PVP after entering a consecutive playthrough on their character.

It is possible that the stone is made from siderite. Siderite is mentioned to be a rare stone that came from the "heavens", which has magnetic properties, and since the Tonsil Stone's description describes it as possibly being a meteorite with "gravitational force."